It happened to me twice, the first time was about 2 years ago on my 2014 GTI, luckly it only knocked the ACC radar housing out of place and I could find it inside the bumper, rattling on the plastic undertray. 3 of the 4 plastic clips that hold it in place were broken but I managed to glue it to the sensor and it worked like that just fine. The second time it happened on the 2016 GTI just a few weeks ago, unfortunately this time the pheasant was pretty big and it f***ed my lower honeycomb grille, the ACC radar housing and two plastic bits from inside the bumper that cover the AC pipes and the left side of the radiator. The pheasant was literally split in half, I spent 1 hour to pull out all the feathers and guts from inside the bumper.
Result: The radar housing was completely gone, couldn't find it in the bumper like the first time, the grille and the plastic bits inside on the radiator where all cracked and broken and the radar sensor itself was out of it's normal position (it has 3 plastic fixing points held in place with 3 bolts which are also used for calibration). The sensor itself was undamaged although I had the Front assist disabled error message on the MFD and the ACC was not working at all. When scanning with VCDS it showed 2 error codes relating to incorrect position of the sensor. I just wiggled it back into the 3 fixing points, it's literally a matter of pushing the sensor back in place and the error was gone after driving 10 miles and the ACC works again.
The housing is pretty cheap, around £5 quid, the part number for GTI/GTD is 5G0 907 225 A 9B9. You can order from any dealer or you can find it on ebay for around £8 as well.
Apart from this I had to order new honeycomb lower grille which was around £35 and the plastic bits inside the bumper were around £12. All in all it cost me £51 in parts. The labour was free as I took the bumper off and swapped the damaged grile and parts myself.